1. Field
This disclosure relates generally to communication systems and, more specifically, to generating bit log-likelihood ratios in communication systems using differential modulation.
2. Related Art
Channel coding or forward error correction (FEC) is a technique used in communication systems for controlling errors in data communication over unreliable or noisy channels. A transmitter of a communication system employing an FEC scheme adds controlled redundancy to an information bit stream. In a receiver, an FEC decoder may exploit the redundancy added in the transmitter while processing the demodulated bits to correct data communication errors. In general, the efficiency of an FEC decoder is improved when, instead of the demodulated hard bits, it is fed soft information which, in some way, manifests the likelihood of each demodulated bit being a ‘0’ or a ‘1’. The soft information of each bit may be calculated as a function of the corresponding demodulated bit/symbol and the estimated noise variance affecting the bit. If the channel is not static but varies in time and/or frequency, the effective noise variance affecting each bit also varies accordingly.
A symbol can be described as a ‘pulse’ in digital baseband transmission or a ‘tone’ in passband transmission using modems that represents an integer number of bits. Theoretically, a symbol is a waveform, a state, or a significant condition of a communication channel that persists for a fixed period of time. In general, a transmitting device transmits a sequence of symbols via a communication channel at a fixed symbol rate and a receiving device detects the sequence of symbols on the communication channel in order to reconstruct transmitted data. In various applications, there may be a direct correspondence between a symbol and a unit of data (e.g., each symbol may encode one or more binary digits or bits), data may be represented by transitions between symbols, or data may be represented by a sequence of symbols.
Channel fading and interference are two examples of factors that cause a channel to vary in time and/or frequency. A communication system designed to work in an environment with channel fading and interference typically provides, in each transmission, a training sequence for obtaining an initial estimate of a channel and pilot sequences interspersed with a data-bearing signal to allow for tracking channel variations. In general, pilot sequences facilitate updating an estimated noise variance and consequently improve FEC decoder performance at the expense of reduced bandwidth efficiency.
A communication system may implement transmitters that use differential modulation instead of providing pilot sequences to conserve bandwidth efficiency when the rate of channel fluctuations is relatively slow compared to symbol duration. In differential modulation, a preceding transmitted symbol acts as reference for a current modulated symbol to facilitate non-coherent demodulation in the receiver.
Smart grid applications communicating over power lines are examples of differentially modulated systems. Power line communication channels are characterized by relatively slow channel variations but are also typically affected by impulse noise and narrow-band interference caused by the operation and switching of appliances, electronics, and other electrical devices connected to a power line. Some narrow-band interference may be present for the entire duration of a communication packet or may arise only for a limited time during a packet. Due to the nature of differential modulation, drastic instantaneous channel fluctuations may cause cascading demodulation errors that lead to significant degradation of soft information provided to an FEC decoder which results in degradation of overall system performance.